I have a close, Muslim cousin who does not perform salah, and does not fast during the holy month of Ramadan. In secret, he does not accept the verdicts of the scholar, but prefers to follow his intellect. He is not concerned with whether his wealth is brought through halal means. He suspects the Qur’an is distorted, and questions a lot of the prophet’s actions, and believes that the Islam that ISIS came with is the same as the one the holy prophet brought. However, openly, if you would meet him, he would seem like any average Muslim, and seem very agreeable to Islamic discourse. He says God-willing, and makes dua to Allah in times of need, praises Allah in good times, and respects the Imams and Ahul-bayt, and he cares about his reputation.

I am very perplexed about this matter. I have no hope of guiding him, as he often lets you hear what you like to hear, but at the same time, he is a cousin of mine, and I know how much Allah puts emphasis on kinship. Please guide me to that which is best

If he do not believe in Quran or Prophet PBUH &F, then on which basis he considers him self Muslim, and on what basis he respects Imams?
You need to make him changehis mind first of all, and realize that he is wrong in his thoughts about Islam, so that he starts to listen.
Otherwise, do not bother your self with him.